I have bought flight tickets with my wife and our baby 5 months old, but I can not make it to flight.
Will there be any problems if only my wife with an infant will fly without me, the baby is registered on my seat.
Call the airline. It's typically not a major problem, but this will be a lot easier if you do some paperwork up front: They should split the reservation into two separate ones, move the baby to your wife's reservation and cancel yours.
This way there is a single reservation for your wife and child that will be flown as booked.